Plasmonic nanoparticles in the quantum regime exhibit characteristic optical properties that cannot be described by classical theories. Time-dependent density functional theory (TDDFT) is rising as a versatile tool for study on such systems, but its application has been limited to very small clusters due to rapidly growing computational costs. We propose an atomistic dipole-interaction-model for quantum plasmon simulations as a practical alternative. Namely the atomic dipole approximation represents induced dipoles with atomic polarizabilities obtained from TDDFT without empirical parameters. It showed very good agreement with TDDFT for plasmonic spectra of small silver clusters at much lower computational cost, though it is not appropriate for molecular-like excitations. It could also reproduce the plasmonic band shift experimentally observed in sub-10 nm silver particles.